Related work: An alternative structural assumption for tractable distributed optimal control of linear systems can be specified in terms of the sparsity and delay patterns of the control system. In particular, it is possible to characterize conditions on the sparsity and delay patterns of the information exchanged between subcontrollers relative to the propagation of signals through sparse and delayed distributed plants such that distributed optimal control is tractable. The seminal paper [1]} introduced the notion of quadratic invariance,We note that spatially invariant systems, as defined in [2]}, also satisfy quadratic invariance. We show in Appendix B that graph symmetric systems and controllers lead to optimal control problems satisfying quadratic invariance. which built upon and generalized funnel causality [3]}, showed that so long as subcontrollers could communicate as quickly as control signals propagated through the plant, then the resulting distributed optimal control problem could be solved via convex optimization. This convex parameterization of sparse and delayed controllers has since been further generalized in the System Level Synthesis (SLS) [4]} and Input-Output Parameterization (IOP) [5]} frameworks, which allow for even richer classes of sparsity and delay patterns to be imposed on distributed controllers.
